Re: Q on turn, likely has me beat, so hero...?
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...and I strongly believe he has the queen.
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If he flipped over Qx, you would have a very marginal fold. You have no more than 5 outs. If the button has a draw, you could have fewer. Assuming you got 2 more bets on the river (and button calls here) you would be getting 9-1 pre-rake; 8.25-1 post-rake.
That also assumes that you will fold unimproved on the river. If you plan to call the river, you need to actually be ahead a significant portion of the time. You "strongly" believe you are behind, so I think this is fold, with calling planning to fold unimproved a very close second.
If "strongly" means 50% and/or there is some chance he would check through a better hand on the river, then it is a call (with the river changed accordingly).
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